A fundamental trait in the
mathematical modeling of continuum physics relies in capturing the essential phenomena of a complex
problem
still keeping
the technical difficulties as manageable as possible. A typical example of this strategy
is provided by classical linear elasticity ([1]})
which, in spite of its very long-lasting tradition, represents yet an unavoidable comparison term even
for the more recent mechanical theories aimed to describe old and new material behaviors that were
not contemplated in the original theory. In particular, the spontaneous creation of singularities like cracks or damages and their evolution process, as well as the dispersive characteristics affecting wave propagation, have originated
a great effort in exploiting new and subtle mathematical formulations, leading to a general consensus on the fact that macroscopic manifestations as plasticity or failure are governed by
intricate mechanisms acting at different scales.
With respect to these considerations, the analysis of the nonlocal
features of a model has become a consolidated strategy towards a better rationale understanding of “how nature works”.
